The FA are reportedly keen for Gareth Southgate to continue as England manager in the wake of their World Cup quarter-final exit.
The 52-year-old led the Three Lions to the last eight of the tournament after taking seven points from nine against the USA, Iran and Wales in Group B before a 3-0 last-16 win over Senegal.
England were handed an unenviable clash with reigning champions France in the quarter-finals and went into the half-time break 1-0 down courtesy of Aurelien Tchouameni's strike.
Harry Kane's penalty gave England hope, but Olivier Giroud restored France's one-goal lead before Kane sent another late penalty over the top of the crossbar, as Southgate's side crashed out.
The former Middlesbrough manager's future is being called into question following their departure from Qatar, although his contract is not due to expire until the end of 2024.
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According to German outlet Bild, the FA have been convinced that Southgate is the right man to lead them forward into the Euro 2024 qualifying cycle, and they want him to stay on.
The report adds that the FA have been left satisfied with England's World Cup run and Southgate's ability to form a "promising" team, which was echoed in a statement by chief Mark Bullingham.
"Gareth and Steve (Holland) prepared the team exceptionally well throughout the tournament. The players were committed to winning the trophy and were very well led by Harry Kane," the statement read.
"But sport can have fine margins and on the day, against the current world champions, it was not to be. This is a very exciting young English squad and, despite the intense disappointment of last night, they should be very proud of their performances in Qatar.
"We are incredibly proud of Gareth, the players, the coaches and the support team and appreciate all the hard work they put in."
Southgate has not been able to end England's 56-year wait for a major tournament trophy in men's football, but he has reached the semi-finals of the 2018 World Cup and final of Euro 2020.
Last year, the 52-year-old became the first England manager since Alf Ramsey in 1966 to lead England to a major tournament final, and only Bobby Robson has also taken the Three Lions to a World Cup semi-final.
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When asked about his future after England's World Cup exit, Southgate admitted that he was having "really conflicted" thoughts, saying: "When I've been through the past few tournaments my emotions have been difficult to really think through properly in those following few weeks.
"I want to make the right decision either way because it has to be the right one to go again, or the right one not to go again and I don't think tonight is the time to make a decision like that. Neither are the next few days really.
"There's lots of things in my head that's really conflicted at the moment, so what I want to make sure, if it's the right thing to say, is that I've definitely got the energy to do that. I don't want to be four, five months down the line thinking I've made the wrong call. It's too important for everybody to get that wrong."
Southgate has now amassed a record of 52 wins, 15 draws and 15 defeats from 82 games in charge of England, and Bild adds that ex-Chelsea boss Thomas Tuchel is the preferred candidate to take over if the 52-year-old leaves.
The FA are said to be willing to consider foreign candidates for the England job, and a move for Leicester City manager Brendan Rodgers has also been mooted.
Should Southgate - who replaced Sam Allardyce as Three Lions boss in 2016 - call time on his England career, the former defender is said to be tempted by a move to the USA.
